Download MathMatters 3 Chapter 2 Lesson 2

MathMatters 3
Chapter 2
Lesson 2-6
Example 1
Solve each inequality and graph its solution on a number line.
a. 2x + 4 < -2
b. 15 ≥ 9 - 3x
Solution
a.
2x + 4
2x + 4 + (-4)
2x
1
1222x
x
< -2
< -2 + (-4)
< -6
1
<122(-6)
< -3
b.
15
15 + (-9)
6
1
1-326
-2
x
Example 2
Graph y ≥ 2x.
Solution
The related equation is y = 2x.
Make a table of values that can be used to
graph the boundary. Note that the boundary
is part of the solution set, and is drawn as a
solid line. To decide which half-plane to
shade, use a test-point not on the boundary.
If it is a solution, then all points on that
half-plane will also be solutions; so, shade
that side. If the point is not a solution, shade
the half-plane that does not contain that test
point.
Test Point: (2, 1)
y ≥ 2x
1 ≥ 2(2)
1 ≥ 4 (false)
Because 1 is not greater than or equal to 4,
shade the half-plane that does not contain
(2, 1).
x
-1
0
1
y
-2
0
2
≥ 9 - 3x
≥ 9 + (-9) - 3x
≥ -3x
1
≤ 1-32(-3x)
≤x
≥ -2
MathMatters 3
Chapter 2
Example 3
1
Graph y > x - 2.
2
Solution
1
The related equation is y = 2x - 2.
Make a table of values that can be used to
graph the boundary. Note that the boundary
is not included in the solution set, and is
drawn as a broken line.
Test Point: (0, 0)
1
y > 2x - 2
1
0 > 2(0) - 2
0 > -2
Because 0 is greater than -2, shade
the half-plane containing (0, 0).
x
-2
0
2
y
-3
-2
-1